Make quests repeatable.

[Mishakai]

...

So far I've skipped all but main story and class/job quests.

I constantly get gold medals for FATES w/o AOE, and w/o a group, not sure what you're doing wrong.
Guildhests, haven't done any, too busy getting xp through other avenues.
Leves might not bring in ZOMG experience, but you get a daily allowance. They aren't worthless unless you craft, they are just more worthwile for crafting classes.
I've gotten more than 2 levels from hunting logs. Heck, the last two mobs in my acn rank 3 netted me 1/2 a level.
Dungeons, the wait will go down as they continue to improve infrastructure.

Clearly you are doing it wrong, or are simply too impatient.